A test consists of 6 multiple choice question | vedclass

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(A) The total number of questions is $n = 6$.We need to choose $4$ questions to be answered correctly out of $6$,which can be done in ${}^{6}C_{4}$ wa

Vedclass · Accepted Answer

$135$

Vedclass · Answer

(A) The total number of questions is $n = 6$.We need to choose $4$ questions to be answered correctly out of $6$,which can be done in ${}^{6}C_{4}$ ways.For each of the $4$ correct questions,there is only $1$ way to choose the correct answer.For each of the remaining $2$ questions $(6 - 4 = 2)$,the candidate must choose an incorrect answer. Since there are $4$ alternatives and only $1$ is correct,there are $3$ incorrect options for each question.Thus,the number of ways is ${}^{6}C_{4} 	imes (1)^4 	imes (3)^2$.${}^{6}C_{4} = \frac{6 	imes 5}{2 	imes 1} = 15$.Number of ways = $15 	imes 1 	imes 9 = 135$.

$A$ test consists of $6$ multiple choice questions,each having $4$ alternative answers of which only one is correct. The number of ways in which a candidate answers all $6$ questions such that exactly $4$ of the answers are correct is:

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